基于多元回归方法计算一般角度射电望远镜反射面的调节——以FAST为例  

Calculating the Adjustment of the Reflective Surface of a General Angle Radio Telescope Based on Multiple Regression Method—Taking FAST as an Example

作　　者：张宇翔 姜永胜[2] 

机构地区：[1]新疆工程学院机电学院,新疆 乌鲁木齐 [2]新疆工程学院数理学院,新疆 乌鲁木齐

出　　处：《应用数学进展》2024年第7期3193-3200,共8页Advances in Applied Mathematics

摘　　要：天文射电望远镜—FAST是继阿雷西博射电望远镜之后全球最大的望远镜。天眼FAST工作原理,它在观测天体时,会随着天体方位的变化,在其500米的基准球面主动反射面上,通过调节主锁点的位置,实时形成工作抛物面。本文在已有的α=0∘, β=90∘的(竖直方向)工作抛物面的计算结果的基础上,分三步实现了对一般角度的主锁点的移动距离。1) 给出α=0∘, β=90∘每一个促动装置沿竖直方向的移动距离。2) 利用此距离,通过多元线性回归方法给出一般角度的工作抛物面的方程。3) 利用主锁点的上下坐标计算每一个主锁点处的空间直线方程,确定空间直线与一般角度的工作抛物面的交点,得出一般角度的主锁点的实际平移距离。计算方法利用实际观测数据进行了验证,结果良好。整个过程方法简单,计算效率高,有一定的推广价值。The Astronomical Radio Telescope FAST is the world’s largest telescope after the Arecibo Radio Telescope. The working principle of Tianyan FAST is that when observing celestial bodies, it will form a working parabolic surface in real-time by adjusting the position of the main locking point on its 500-meter reference spherical active reflection surface as the orientation of the celestial body changes. On the basis of the calculation results of the existing (vertical) working parabolic surface, this article implements the movement distance of the main locking point for general angles in three steps. 1) Provide the vertical movement distance of each actuator. 2) Using this distance, the equation for a general angle working parabolic surface is given using the multiple linear regression method. 3) The spatial line equation at each main locking point is calculated using the upper and lower coordinates of the main locking point, and the intersection point between the spatial line and the general angle working parabolic surface is determined to obtain the actual translation distance of the general angle main locking point. The calculation method was validated using actual observation data, and the results were good. The entire process is simple, computationally efficient, and has a certain promotional value.

关 键 词：工作抛物面 多元线性回归 方向余弦 

分 类 号：G63[文化科学—教育学]